The interaction of amphiphilic polymers with small colloids, capable to reversibly stick onto the chains, is studied. Adhesive small colloids in solution are able to dynamically bind two polymer segments. This association leads to topological changes in the polymer network configurations, such as looping and cross-linking, although the reversible adhesion permits the colloid to slide along the chain backbone. Previous analyses only consider static topologies in the chain network. We show that the sliding degree of freedom ensures the dominance of small loops, over other structures, giving rise to a new perspective in the analysis of the problem. The results are applied to the analysis of the equilibrium between colloidal particles and star polymers, as well as to block copolymer micelles. The results are relevant for the reversible adsorption of silica particles onto hydrophilic polymers, used in the process of formation of mesoporous materials of the type SBA or MCM, cross-linked cyclodextrin molecules threading on the polymers and forming the structures known as polyrotaxanes. Adhesion of colloids on the corona of the latter induce micellization and growth of larger micelles as the number of colloids increase, in agreement with experimental data.
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